BRUSSELS—Depositors in Cypriot banks will be hit with a one-off tax on their savings, as part of a €10 billion ($12.96 billion) bailout for the Mediterranean island from the euro zone and the International Monetary Fund.

The deal, announced early Saturday, marks the first time in the euro zone's five-year-old financial crisis that depositors in bloc's banks will lose money. Accounts with more than €100,000 will be taxed at 9.9%, those...